Highest Common Factor (H.C.F) : It is also called
Greatest common Diviser (G.C.D). When a greatest number
divides perfectly the two or more given numbers then that
number is called the H.C.F. of two or more given numbers.
e.g.
The H.C.F of 10, 20, 30 is 10 as they are perfectly
divided by 10,5 and 2 and 10 is highest or greatest of
them.
Least common Multiple (L.C.M.) : The least number
which is divisible by two or more given numbers, that least
number is called L.C.M. of the numbers.
L.C.M. of 3,5,6 is 30, because all 3 numbers divide
30, 60, 90, ...... and so on perfectly and 30 is minimum of
them.
Factor and Multiple : If a number m, divides perfectly
second number n, then m is called the factor of n and n is
called the multiple of m.
Rule 1 : 1st number × 2nd number = L.C. M. × H.C.F.
l There are two methods for calculating the H.C.F
and L.C.M.
(i) Factor Method
(ii) Division Method
l If the ratio of two numbers is a:b, (lowest form i.e.
indivisible to each other) then
Numbers are ak and bk, where k is a constant and
hence,
H.C.F. is K and L.C.M. is abk
Rule 2 :
L.C.M of fractions=L.C.M.of numerators/
H.C.F.of denominators
Rule 3 :
H.C.F. of fractions=H.C.F of numerators/
L.C.M.of denominators
l If there is no common factor between two numbers,
then L.C.M. will be the product of both numbers.
l If there are ‘n’ numbers in a set and H.C.F. of any two
numbers is H and L.C.M. of all ‘n’ numbers is L, then
product of all ‘n’ numbers is [(H)^n-1×L].